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0580/42 Feb/Mar 2021, Question 9: Expand and Simplify

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Algebra question: factorise three expressions, expand and simplify a product of three brackets, and find a and b in an identity.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 2 marks

Factorise 5am + 10ap − bm − 2bp by grouping.

  1. 15am + 10ap − bm − 2bp = 5a(m + 2p) − b(m + 2p)
  2. 2= (5a − b)(m + 2p)

Answer(5a − b)(m + 2p)

Part (aii) · 2 marks

Factorise 15(k + g)² − 20(k + g) by taking out the common factor.

  1. 1Common factor 5(k + g)
  2. 215(k + g)² − 20(k + g) = 5(k + g)(3(k + g) − 4)
  3. 3= 5(k + g)(3k + 3g − 4)

Answer5(k + g)(3k + 3g − 4)

Part (aiii) · 2 marks

Factorise the difference of two squares 4x² − y⁴.

  1. 14x² − y⁴ = (2x)² − (y²)² (difference of two squares)
  2. 2= (2x − y²)(2x + y²)

Answer(2x − y²)(2x + y²)

Part (b) · 3 marks

Expand and simplify (x − 3)(x + 1)(3x − 4).

  1. 1(x − 3)(x + 1) = x² − 2x − 3
  2. 2(x² − 2x − 3)(3x − 4) = 3x³ − 4x² − 6x² + 8x − 9x + 12
  3. 3= 3x³ − 10x² − x + 12

Answer3x³ − 10x² − x + 12

Part (c) · 2 marks

Given (x + a)² = x² + 22x + b, find the values of a and b.

  1. 1(x + a)² = x² + 2ax + a²
  2. 22a = 22 so a = 11
  3. 3b = a² = 121
  4. 4a = 11, b = 121

Answera = 11, b = 121

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Also searched as: 0580/42/F/M/21 · 0580_m21_qp_42 · 0580 m21 42 · question 9.
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